C₁₃×#2096 #13111154

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#2096

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

254 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,23)(20,24,25,22)(26,27,31,33,30,28,29,32);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(26,28,30,27)(29,32,31,33);(15,17)(26,27,30,28)(29,33,31,32)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15750531, #15752043, #15752049, …
maximal subgroup of	C₁₃×#7437, C₁₃×#7801, C₁₃×#7802, …
maximal normal subgroup of	C₁₃×#7437, C₁₃×#7801, C₁₃×#7802, …
maximal quotient of	C₁₃×#10663, C₁₃×#10670, C₁₃×#10675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 828);